\contentsline {section}{\numberline {1}Introduction}{6}
\contentsline {section}{\numberline {2}Background}{9}
\contentsline {subsection}{\numberline {2.1}Emergent Behaviour}{9}
\contentsline {subsection}{\numberline {2.2}Methods for Modelling Emergent Behaviour in Finance}{12}
\contentsline {subsubsection}{\numberline {2.2.1}Recurrence Relations}{12}
\contentsline {subsubsection}{\numberline {2.2.2}Agent-Based Models}{13}
\contentsline {subsection}{\numberline {2.3}InterDyne}{15}
\contentsline {subsubsection}{\numberline {2.3.1}Applicability to Finance}{16}
\contentsline {paragraph}{\numberline {2.3.1.1}Deterministic}{16}
\contentsline {paragraph}{\numberline {2.3.1.2}Message Delays}{16}
\contentsline {paragraph}{\numberline {2.3.1.3}Storing Messages}{16}
\contentsline {paragraph}{\numberline {2.3.1.4}Message Ordering}{16}
\contentsline {subsubsection}{\numberline {2.3.2}InterDyne Detailed Operation}{17}
\contentsline {section}{\numberline {3}Description and Analysis of the Problem}{20}
\contentsline {subsection}{\numberline {3.1}Method for Achieving a Translation}{20}
\contentsline {subsection}{\numberline {3.2}Review of Similar Work}{21}
\contentsline {subsection}{\numberline {3.3}Challenges with the Translation Approach}{23}
\contentsline {section}{\numberline {4}Bespoke Recurrence Relation Language}{25}
\contentsline {subsection}{\numberline {4.1}Syntax}{25}
\contentsline {subsection}{\numberline {4.2}Naming Conventions}{28}
\contentsline {subsection}{\numberline {4.3}Well Formed Programs}{29}
\contentsline {section}{\numberline {5}Design of a Translation from Recurrence Relations to InterDyne}{32}
\contentsline {subsection}{\numberline {5.1}Infinite List Output}{33}
\contentsline {subsection}{\numberline {5.2}Grouping into Agents}{35}
\contentsline {subsection}{\numberline {5.3}A Global Output List}{36}
\contentsline {subsection}{\numberline {5.4}Agent Input Lists}{39}
\contentsline {subsection}{\numberline {5.5}Targeted Information Passing}{42}
\contentsline {subsection}{\numberline {5.6}A Simulator Harness}{47}
\contentsline {subsection}{\numberline {5.7}Runtime Arguments}{51}
\contentsline {subsection}{\numberline {5.8}Message Communication}{55}
\contentsline {section}{\numberline {6}Validation and Testing}{61}
\contentsline {subsection}{\numberline {6.1}Translation Validation}{61}
\contentsline {subsection}{\numberline {6.2}Translation Semantic Considerations}{62}
\contentsline {subsection}{\numberline {6.3}Automated Translation Implementation}{63}
\contentsline {section}{\numberline {7}Summary and Conclusion }{66}
\contentsline {subsection}{\numberline {7.1}Discussion and Further work }{67}
\contentsline {section}{Appendix A: Program for Numerical Testing}{69}
\contentsline {section}{Appendix B: Implementation of Translation}{83}
\contentsline {section}{References}{91}
